Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class codeforces{
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public String nextLine() {
            String s = null;
            try {
                s = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return s;
        }
 
        public String nextParagraph() {
            String line = null;
            String ans = "";
            try {
                while ((line = reader.readLine()) != null) {
                    ans += line;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return ans;
        }
    }
    static long mod = 1000000007;
    static void printArray(int ar[]){ for(int x:ar) System.out.print(x+" ");}
    static void printArray(ArrayList<Integer> ar){ for(int x:ar) System.out.print(x+" ");}
    static int gcd(int a, int b){ if (a == 0) return b; return gcd(b%a, a);}
    static class Data{
        int e;
        String val;
        public Data(int e,String val){
            this.e = e;
            this.val = val;
        }
    }
    public static void main(String args[]){
        InputReader sc = new InputReader();
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = (n / 2) + 1;
        int i=1, j=1;
        pw.println(m);
        for(int x=1;x<=n;x++){
            pw.println(i+" "+j);
            if(x%2 != 0)
                j++;
            else i++;
        }
        pw.close();
    }
}